Abstract
We show that the number of lattice directions in which a d- dimensional convex body in Rd has minimum width is at most 3d -1, with equality only for the regular cross-polytope. This is deduced from a sharpened version of the 3d-theorem due to Hermann Minkowski (22 June 1864-12 January 1909), for which we provide two independent proofs.
Original language | English |
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Publisher | s.n. |
Number of pages | 10 |
Publication status | Published - 2009 |
Publication series
Name | arXiv.org [math.CO] |
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Volume | 0901.1375 |